Finite Group Databasebeta

C2×C8×C4⋊#261 #16797116

order3328
isoclinismisoclinic class of #6118
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C8×C4⋊#261

Splittings

FittingC2×C4×C8×C13 ⋊ C4
SylowC13 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC22×C8C2×#261
commutatorC2×C13C22×C4×C8
FrattiniC2×C4C23×#261
FittingC2×C4×C8×C13C4
socleC23×C13C2×C42
prime radicalC23×D13C22×C4
cosocleC2×C4×D13C24
hypercenterC2×C4×C8#261
hypocenterC13C2×C8×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103765);